18.03SC Practice Problems 24
Step and delta functions
⎧
0
⎪
⎪
⎨
2t − 2
1. Let Q(t) =
−1
2t
⎪
⎪
⎩
5
for t < 1
for 1 < t < 2
for 2 < t < 3
for 3 < t
(a) Sketch a graph of this function. Is it piecewise smooth?
(b) Find the generalized derivative q(t) = Q� (t), and sketch it.
(c) Describe a scenario which might be modeled by the equation ẋ + kx = q(t)
(your choice of k) with rest initial conditions.
(d) Describe a scenario which might be modeled by the equation 2ẍ + 4ẋ + 4x =
q(t) with rest initial conditions.
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